Seminario di analisi matematica
ore
16:00
presso Aula Enriques
The curve shortening flow is an evolution equation in which a curve moves with normal velocity equal to its curvature,
and can be interpreted as the gradient flow of the length.
In this talk I will consider the same flow for networks (finite unions of sufficiently smooth curves whose
endpoints meet at junctions).
I will explain how to define the flow in a classical PDE framework, and then I will list some examples of singularity formation,
both at finite and infinite time, and explain the resolution of such singularities obtained by geometric microlocal analysis
techniques.
I will describe a stability result based on Lojasiewicz–Simon gradient inequalities and give a rough estimate
on the basin of attraction of critical points. Furthermore, I will motivate the coarsening-type behavior
clearly visible in numerical simulations.
This seminar is mainly based on recent papers in collaboration with Jorge Lira (Uni-
versidade Federal do Ceará), Rafe Mazzeo (Stanford University), Mariel Saez (P. Universidad
Catolica de Chile) and Marco Pozzetta (Università di Napoli Federico II).